Abstract
In this article, we investigate a structure-preserving finite difference scheme to the thermo-visco-elasto-plastic system in a one-space dimension under a perfect elasto-plasticity represented by the stop operator. We introduce the structure-preserving finite difference scheme for the system which satisfies the energy conservation law, momentum conservation law and the increasing law of entropy in the discrete sense. The main purpose of this article is to give mathematical treatment such as the existence of solution and error estimate for the scheme, under the assumption of uniformly distributed temperature with respect to space. In addition, several numerical simulations are also demonstrated as examples.
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